Data was available only upon request

Data was available only upon request. novel extension to the Gillespie algorithm that enables the efficient stochastic simulation of the system, while keeping track of individual cell properties. Our model is able to explain the dynamical shift from memory B cell to plasma cell production over the lifetime of a GC. Moreover, our results suggest that B cell fate selection can be explained as a process that depends fundamentally on antigen affinity. account, respectively for IRF4 basal transcription rate, induced transcription rate, degradation, and DNA dissociation constant. Their experimentally determined values are detailed in Table S1 in the Supplementary Information. In the above equation, and Regarding antigen, any amount acquired from previous interactions with FDCs is divided equally among the daughter cells. We examine later on in this paper an alternative scenario, where one daughter cell inherits all antigen (see discussion in section 4). 2.2.3. Antigen Uptake PPP1R53 CCs that (S)-Tedizolid encounter FDCs might acquire antigen if their BCRs bind with enough affinity to the antigen. Our model assumes that all FDCs carry the same amount of antigen, which is exposed on their surface. We assume (S)-Tedizolid that antigen can only be acquired from the FDCs and the amount presented reflects the concentration of antigen complexes in the extracellular milieu (3). Our model does not explicitly simulate FDC dynamics, but considers that antigen uptake occurs when a CC encounters an FDC through the following reaction channel: or are the experimentally determined normalized counts of PCs and MBCs that exit the GC over a period of 30 days, as measured by Weisel et al. (17), and are the respective model predictions. The criterion defined by Equation (12) aims to minimize differences in means and standard deviations between experimentally measured and computed counts. The optimization was performed using maxLIPO from dlib (38). 4. Results 4.1. T Cell Help Is Crucial for Affinity Maturation and PC Production Stochastic simulations with the parameters found in the literature proved to be unstable, with all populations vanishing by day 10 (see Figure S2). A deterministic analysis (see SI) revealed that the ratio tightly controls the regime of stability. A numerical stochastic exploration of the stability bounds of the fitted parameters revealed the following condition for a stable regime: Inserting the parameters into the constraints found in the deterministic analysis yielded the same bounds within a deviation of 1%. These bounds explain why the set of parameters derived from the literature did not lead to stable populations: The parameters found in the literature result in a ratio of on (S)-Tedizolid average to encounter a T cell. This large waiting time is higher than the mean life-time of a CC before it dies through apoptosis, which has been estimated to be ~10(27). Hence, for these parameters, an average CC does not have enough time to find a T cell and efficiently compete for survival signals. To demonstrate the importance of allowing for enough time for CCs to encounter and interact with T cells, we performed an additional simulation where we increased three-fold rT cell encounter (see Figure S3). As it is evident in this figure, the fraction of bounded T cells increases to 80 %, leading to a system that exhibits affinity maturation with time. However, affinity maturation is slow, resulting in a noticeable output of MBCs at late time points and a slow increase of the PC output with time, which only starts reaching steady state at day 30, in disagreement with experimental observations (17). Open in a separate window Figure 2 GC cellular populations over time for the set of stabilized literature parameters. The parameters calculated from evidence in the literature, adjusted to lead to stable populations. Affinity does not increase over time, MBC output is still significant at day 30 and PC output only.